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Automorphism — In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms… … Wikipedia

automorphism — noun An isomorphism of a mathematical object or system of objects onto itself … Wiktionary

Outer automorphism group — In mathematics, the outer automorphism group of a group G is the quotient Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually … Wikipedia

Inner automorphism — In abstract algebra an inner automorphism is a function which, informally, involves a certain operation being applied, then another one (x) performed, and then the initial operation being reversed. Sometimes this has a net effect ( take off shoes … Wikipedia

Family automorphism — In mathematics, in the realm of group theory, an automorphism of a group is termed a family automorphism if it takes every element to an element generating a conjugate subgroup. In symbols, an automorphism sigma of a group G is a family… … Wikipedia

Extensible automorphism — In mathematics, an automorphism of a structure is said to be extensible if, for any embedding of that structure inside another structure, the automorphism can be lifted to the bigger structure.In group theory, an extensible automorphism of a… … Wikipedia

Class automorphism — In mathematics, in the realm of group theory, a class automorphism is an automorphism of a group that sends each element to within its conjugacy class. The class automorphisms form a subgroup of the automorphism group. Some facts: Every inner… … Wikipedia